Some Remark on Optimal Stochastic Control with Partial Information

Abstract

We are interested in the control problem of a partially observable diffusion process, which is initialized at a fixed point of ? ⁿ , and we want to characterize the associated value function. To resort to the theory of viscosity solutions depends on the possibility to translate such a problem on Hilbert spaces like L ²(? ⁿ ), and so it can not be used here. Nevertheless, a result of N. Bouleau and F. Hirsch allows us to introduce a broadened problem which fulfills the condition. The fact remains to link these two control problems.     

Convenient Synthesis of 2-Aminothiophene Derivatives by Acceleration of Gewald Reaction Under Ultrasonic Aqueous Conditions

Under ultrasound irradiation and in the presence of H₂O/Et₂NH, ethyl cyanoacetate or malononitrile can combine with α-methylene carbonyl compounds and elemental sulfur to efficiently yield 2-aminothiophene derivatives within a few minutes. Products are easily obtained by simple filtration because of their spontaneous precipitation in the reaction mixtures.     

A highly diastereoselective five-component synthesis of 1-(alkylimino)-5,5-dicyano-3a-aryloctahydro-3-oxacyclobuta[cd]pentalene-1a,2,5a,5b(2H,3aH)-tetracarboxylates

A novel one-pot, five-component synthesis of 1-(alkylimino)-5,5-dicyano-3a-aryloctahydro-3-oxacyclobuta[cd]pentalene-1a,2,5a,5b(2H,3aH)-tetracarboxylates is described. A mixture of phenacyl bromide, malononitrile, isocyanide, and two equivalents of a dialkyl acetylenedicarboxylate undergoes a novel 1:1:1:2 addition reaction at ambient temperature in absolute ethanol to produce diastereoselectively the title compounds in good yields.     

Indium‐Bridged [1]Ferrocenophanes

Indium‐bridged [1]ferrocenophanes ([1]FCPs) and [1.1]ferrocenophanes ([1.1]FCPs) were synthesized from dilithioferrocene species and indium dichlorides. The reaction of Li₂fc?tmeda (fc=(H₄C₅)₂Fe) and (Mamx)InCl₂ (Mamx=6‐(Me₂NCH₂)‐2,4‐tBu₂C₆H₂) gave a mixture of the [1]FCP (Mamx)Infc ( 4₁ ), the [1.1]FCP [(Mamx)Infc]₂ ( 4₂ ), and oligomers [(Mamx)Infc]_n ( 4 _n ). In a similar reaction, employing the enantiomerically pure, planar‐chiral (S_p,S_p)‐1,1′‐dibromo‐2,2′‐diisopropylferrocene ( 1 ) as a precursor for the dilithioferrocene derivative Li₂fc^iPr2, equipped with two iPr groups in the α position, gave the inda[1]ferrocenophane 5₁ [(Mamx)Infc^iPr2] selectively. Species 5₁ underwent ring‐opening polymerization to give the polymer 5 _n . The reaction between Li₂fc^iPr2 and Ar′InCl₂ (Ar′=2‐(Me₂NCH₂)C₆H₄) gave an inseparable mixture of the [1]FCP Ar′Infc^iPr2 ( 6₁ ) and the [1.1]FCP [Ar′Infc^iPr2]₂ ( 6₂ ). Hydrogenolysis reactions (BP86/TZ2P) of the four inda[1]ferrocenophanes revealed that the structurally most distorted species ( 5₁ ) is also the most strained [1]FCP.     

A handy proof of Gay's theorem

In 1979, Gay proved that Broyden's methods, when used for n‐square linear systems, terminate in at most 2n iterations (SIAM J. Numer. Anal. 1979; 16 :623–630). Also, the ABS methods were introduced in 1984 (Numer. Math. 1984; 45 :1361–1376). In this paper we show another (handy) proof of Gay's theorem by these algorithms. Copyright © 2008 John Wiley & Sons, Ltd.     

An efficient synthesis of 3-amino-2-arylimidazo[1,2-a]pyridines

An efficient synthesis of 3-amino-2-arylimidazo[1,2-a]pyridines is described via a novel multicomponent reaction between 2-aminopyridines, benzaldehydes and imidazoline-2,4,5-trione under solvent-free conditions.     

A Multilevel Shape Fit Analysis of Neutron Transmission Data

A multilevel shape fit analysis of neutron transmission data is presented. A multilevel computer code SHAPE is used to analyse clean transmission data obtained from time-of-flight (TOF) measurements. The shape analysis deduces the parameters of the observed resonances in the energy region considered in the measurements. The shape code is based upon a least square fit of a multilevel Briet-Wigner formula and includes both instrumental resolution and Doppler broadenings. Operating the SHAPE code on a test example of a measured transmission data of ¹⁵¹Eu, ¹⁵³Eu and natural Eu in the energy range 0.025-1 eV accquired a good result for the used technique of analysis.     

An unusual bioactive oleanane triterpenoid from Rhododendron campanulatum D.Don

An unusual oleanane triterpene(1) was isolated from aerial parts of Rhododendron campanulatum.The compound had shown prominent antibacterial and immunomodulatory activities.The structure of the compound was determined by spectroscopic data including 1D and 2D NMR spectral analysis.     

Facile One‐Pot Three‐Component Synthesis of Functionalized Pyridylfuran‐2‐amines

The reactive 1 : 1 zwitterionic intermediates generated in situ from the reaction between a series of isocyanides and diaroylacetylenes were trapped by pyridine carbaldehydes to yield highly functionalized 5‐pyridylfuran‐2‐amines in good yields (82–93%).     

Self‐Healing Polyester Urethane Supramolecular Elastomers Reinforced with Cellulose Nanocrystals for Biomedical Applications

Stretchable self‐healing urethane‐based biomaterials have always been crucial for biomedical applications; however, the strength is the main constraint of utilization of these healable materials. Here, a series of novel, healable, elastomeric, supramolecular polyester urethane nanocomposites of poly(1,8‐octanediol citrate) and hexamethylene diisocyanate reinforced with cellulose nanocrystals (CNCs) are introduced. Nanocomposites with various amounts of CNCs from 10 to 50 wt% are prepared using solvent casting technique followed by the evaluation of their microstructural features, mechanical properties, healability, and biocompatibility. The synthesized nanocomposites indicate significantly higher tensile modulus (approximately 36–500‐fold) in comparison to the supramolecular polymer alone. Upon exposure to heat, the materials can reheal, but nevertheless when the amount of CNC is greater than 10 wt%, the self‐healing ability of nanocomposites is deteriorated. These materials are capable of rebonding ruptured parts and fully restoring their mechanical properties. In vitro cytotoxicity test of the nanocomposites using human dermal fibroblasts confirms their good cytocompatibility. The optimized structure, self‐healing attributes, and noncytotoxicity make these nanocomposites highly promising for tissue engineering and other biomedical applications.